CITES was formed in 1973 and to date has 163 members. Membership is voluntary as is adhesion to the aims and ambitions. (cites.org)
Trading internationally is not the same as one person purchasing from another, a single item. CITES is about the exploitation of endangered species. Permits for single items, such as bracelets are not required according to the CITES directorate in Pretoria.
It is true that CITES is for the protection of endangered animals (and plants). It was designed to control and prevent the trade in the live or dead animals and live plant samples or the slaughter of animals for their hide or in this case the ivory tusks.
Many people in Southern Africa, especially Zimbabwe and KZN in South Africa produce products from animal by-product which is what most elephant hair is. It is just not profitable to poach animals to manufacture a small bracelet. All workshops that I am aware of in South Africa are permitted to manufacture and they can be found openly on sale in the gift and souvenier shops.
For those who wish to be sure that what they buy does not come from animals, there are a number of people who offer imitation bracelets made from dried River Reed or other animal hair, not within the CITES remit which can be purchased, such as Giraffe.
There are numerous people offering genuine elephant hair bracelets and as far as I can see most demonstrate a high degree of integrity. If in any doubt contact them before making your purchase, try to find out the source of the product. Ask questions!